This question is a bit different from other questions here, but I think it is suitable to correctly understand the terminology of cryptography.

Consider the following two sets of terms:

Encryption scheme, signature scheme

Identification scheme, commitment scheme, secret-sharing scheme

The latter are actually "protocols", while we usually do not consider encryption/signature as (interactive) "protocols". Moreover, the word "scheme" is not usually applied to terms like "hash functions", "pseudo-random generators", "one-way functions", etc.

What does the term "scheme" mean? When is it meaningful to apply this term to a cryptographic construct? How does it relate to "protocols"?

As @mikeazo correctly states, I don't think there is any formal or precise definition for the term "scheme". It is probably used loosely in a way that might well mean a "protocol", "mode of operation", "cryptosystem", "cryptographic algorithm", or even something else entirely.